OFFSET
1,1
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
The reverse-alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^(k-i) y_i. Of course, the reverse-alternating sum of prime indices is also the alternating sum of reversed prime indices.
EXAMPLE
The initial terms and their prime indices:
2: {1}
6: {1,2}
8: {1,1,1}
15: {2,3}
18: {1,2,2}
24: {1,1,1,2}
32: {1,1,1,1,1}
35: {3,4}
50: {1,3,3}
54: {1,2,2,2}
60: {1,1,2,3}
72: {1,1,1,2,2}
77: {4,5}
96: {1,1,1,1,1,2}
98: {1,4,4}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
sats[y_]:=Sum[(-1)^(i-Length[y])*y[[i]], {i, Length[y]}];
Select[Range[100], sats[primeMS[#]]==1&]
CROSSREFS
The k > 0 version is A000037.
These multisets are counted by A000070.
The version for unreversed-alternating sum is A001105.
These partitions are counted by A035363.
These are the positions of 1's in A344616.
A025047 counts wiggly compositions.
A027187 counts partitions with reverse-alternating sum <= 0.
A097805 counts compositions by alternating (or reverse-alternating) sum.
A316524 gives the alternating sum of prime indices.
A344606 counts alternating permutations of prime indices.
A344607 counts partitions with reverse-alternating sum >= 0.
A344610 counts partitions by sum and positive reverse-alternating sum.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 11 2021
STATUS
approved